Ch. 15--ANOVA

1. Use of flow chart

2. Overview

3. The F test

a. sampling distribution of F

b. F table

c. when to use the F test

i. more than 2 groups

i. F vs. Multiple t-tests

4. Generating Hypotheses for ANOVA

5. Calculating the statistic

a. Conceptual F

i. Total Variance

ii. Between-group variance

iii. Within group variance

iv. Fobt = s_{b}^{2}/ s_{w}^{2}

b. Calculating Fobt

__Source of variance SS df s ^{2} (MS) Fobt__

Between groups formula k-1 Ss_{b} / df_{b} s_{b}^{2}/ s_{w}^{2}

Within groups formula N-k Ss_{w} / df_{w}

Total Formula N-1

SSb =

SSw =

SSt =

Example

is there a difference exam scores as a function of teaching style? 3 different teachers.

X1 X2 X3

52 46 44

57 52 53

55 51 50

59 50 51

6. Evaluating Fobt--compare with fcrit

7. Comparison between F and t

i. testing means

ii. t^{2} = F

8. Assumptions of ANOVA

i. normal distribution

ii. Homogeneity of variance

iii. Robust

9. Two-way, or Factorial ANOVA

i. Factorial experiment: when two or more factors are assessed

ii. Use a two-way ANOVA

iii. Components to understand:

a. main effects= effect of one IV independent of the other

b. interaction= when the effect of one IV is not the same at all levels of the other IV

iv. F's for main effects

a. IV1 : F = s_{r}^{2} /s_{w}^{2}

b. IV2 F = s_{c}^{2} /s_{w}^{2}

c. Interaction: F = s_{rc}^{2} /s_{w}^{2}